Question

a particle executes SHM of amplitude 25cm and time period 3sec.what is the minimum time required for the particle to move between two points 12.5cm on either side of the mean position?

Answer 1

hope u understand the calculations yourself

Answer 2

time required for the particle would be 0.5 sec

given, amplitude, A = 25cm

time period, T = 3sec

so, equation of particle executing SHM, y = Asin(2πt/T)

= (25cm)sin(2πt/3 )

we have to find the time required for the particle to move between two points 12.5 cm on either side of the mean position.

so, distance travelled by particle from one point to mean position, y = 12. 5cm

now, y = 12.5cm = (25cm)sin(2πt/3)

⇒1/2 = sin(π/6) = sin(2πt/3)

⇒π/6 = 2πt/3

⇒t = 1/4 sec

similarly, time taken to travel by particle from mean to other point , t = 1/4 sec

so, total time required , t' = 2t = 2 × 1/4 sec = 1/2 sec

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